CH-17-001 · Chord geometry and a minor segment
A circle has centre O and radius 39 cm. AB is a chord. M is the midpoint of AB and OM = 30 cm. Calculate the length AB and the area of the minor segment above AB. Give both answers to 2 decimal places.
Circle Chord Geometry, Pythagoras, SOH CAH TOA & Shaded Segment
Booklet p. 34, p. 37 & p. 38
Method
1) Line from centre O to midpoint M of chord is perpendicular (90°)
2) Use Pythagoras for AM and AB = 2AM
3) Use CAH for angle AOB, then Sector − Triangle
Worked Example (CH-17-001)
1)
OM is perpendicular to AB; a line from the centre to the midpoint of a chord is perpendicular to the chord.
2)
AM = √(39² − 30²).
3)
AB = 49.84 cm.
4)
Angle AOB = 2 cos⁻¹(30/39) = 79.43027…°.
5)
Segment area = sector area − triangle area; use full precision.
6)
306.70 cm².
Ans =
AB = 49.84 cm; segment area 306.70 cm².